Certainly things like sugar & alcohol are just poisons for the body, and when you eliminate them your body feels better and you have more energy all the time, so part of the happiness is from that. And if you eliminate things like TV and interent browsing, you're forced to do more substantial activities for pleasure like meeting new people and getting out of the house and so on, so part of the happiness is from that.
But I think a major aspect of it is human happiness renormalization.
If you allow yourself to have these "bumps" of very high pleasure from sugar, alcohol, drugs, porn, lolcats, whatever, then in comparison everything else feels pretty awful. You can fall into this mindset that "life sucks, except for the bumps".
If you cut out all those highs, at first you're just miserable for a while, but then your brain renormalizes, and lots of little things become pleasurable. Reading a book, watching the sunrise, the feel of cloth on your skin, taking a walk. Suddenly those things are very high pleasures, because you're not allowing yourself anything higher.
I suspect that if you went fully ascetic like a monk and ruled out sex and ate only rice, and forced yourself to do something deeply miserable like meditate for two hours a day (there's almost nothing in life that's more painful than meditation), then in contrast just sitting and talking to someone would be an ecstatic pleasurable experience, and you would be constantly full of joy like the Dalai Fucking Lama.
The closest experience I have is backpacking, which makes returning to hot food and a comfy bed so magical and amazing. Asceticism is a bit like backpacking every day; it makes ordinary life magical and amazing.